The present invention relates to CDMA (Code Division Multiple Access) spread spectrum receivers, and more particularly to tracking in fast acquisition GPS (Global Positioning System) receivers.
Spread spectrum communication in its basic form is a method of taking a data signal used to modulate a sinusoidal carrier and then spreading its bandwidth to a much larger value, e.g. in a global positioning system (GPS) application, by multiplying a single-frequency carrier by a high-rate binary (xe2x88x921,1) pseudo-random noise (PRN) code sequence known to GPS users. Thus, the signal that is transmitted includes a data component, a PRN component, and a (sinusoidal) carrier component.
At the receiver, a synchronized replica of the transmitted PRN code is required to de-spread the data sequence. Initial synchronization, called acquisition, is followed by fine synchronization, which is called tracking.
In a ranging receiver used by a user to determine the position of the user based on the distance of the receiver from GPS satellites, in good signal conditions a range measurement called pseudorange is determined from information provided by tracking channels of the receiver and also from navigation data sent by each of the satellites and decoded by the receiver.
The GPS positioning system relies on the ranging receiver being able to reference to one clock the time when it receives ranging signals from each of the different satellites, and the time the GPS satellites transmitted the ranging signals (and more specifically, a particular fragment of a ranging signal, called here the target signal fragment). The ranging receivers do not, however, as a matter of economics, use clocks that can be synchronized with the clock used by the GPS or the clocks used by the different GPS satellites. The clocks of ranging receivers are based on relatively inexpensive oscillators whose frequency varies, changing permanently in some situations, and changing only temporarily in others. Some causes are categorized as deterministic or causal (e.g. temperature, causing a time-varying error; in crystal clocks, imperfections in the crystal used by the clock, causing a constant error, and aging of the crystal, causing an error that increases or decreases monotonically with time; magnetic fields, causing a time-varying error; and systematic drift in clocks besides only crystal clocks) and some as non-deterministic (i.e. random or noise-like causes, such as random walk and so-called flicker noise).
In many navigation systems, Kalman filtering or similar techniques are used to determine a track for a receiver in which errors due to deficiencies in the local oscillator (and due to other sources of error as well) are smoothed out. The tracking is performed by having one or another type of navigation filter use an appropriate model of clock behavior. Conventional models of clock behavior are usually based on random, noise-like changes in frequency measured in the time domain; systematic changes are interpreted as random fluctuations (albeit on a longer time scale than actual random fluctuations), and the process covariance matrix in state equations used by the navigation filter is changed to account for such fluctuations.
What is needed is an improved model of clock behavior for use by a navigation filter (such as a Kalman filter), a model that incorporates systematic changes in frequency due to systematic causes, such as for example temperature or other environmental effects, not as random fluctuations, but as actual systematic changes.
Accordingly, in a first aspect of the invention, a method is provided for estimating a current state of a clock having a clock phase indicating a value for time, the method including: a step of providing a clock measurement indicating information about the clock; and a step, responsive to the clock measurement, for determining the estimate of a current state of the clock using a state filter adapted to use a four-component state including as components a clock phase component and a clock fractional frequency component, and also including a clock error component and a clock error rate component, and further adapted to use a measure of four-state process noise covariance.
In accord with the first aspect of the invention, the clock measurement may indicate information about the clock phase and clock fractional frequency. Further, the measure of process noise covariance may be a process noise covariance matrix, and the process noise covariance matrix may include as diagonal terms respective variances in the values for each of the four components of the four-component state. Still further, the four-state process noise covariance matrix may be based on a definition of a process noise covariance matrix Q given by,
Q=E(wkwkt)
where E( . . . ) indicates taking the mathematical expectation of the indicated argument, and where the wk is a four-component vector indicating process noise. Also, still even further, the four-state process noise covariance matrix may be derived from a two-state process noise covariance for a two-state clock model in a way that preserves the components of the process noise covariance for the two-state clock model, regardless of the manner in which the components of the process noise covariance for the two-state clock model are defined. In other applications where the clock measurement indicates information about the clock phase and clock fractional frequency, the state of the ranging receiver may include as components the clock phase component, the clock fractional frequency component, the clock error component, and the clock error rate component, and may also include either a position component or a velocity component indicating either the position or velocity of the ranging receiver, respectively.
Also in accord with the first aspect of the invention, the step for determining the estimate of a current state of the clock may be performed as part of a step of providing an estimate of a current state of a ranging receiver used in conjunction with beacons of a positioning system, and the method may further comprise a step of providing pseudoranges from the beacons of the positioning system.
In a second aspect of the invention, a clock system is provided for giving an estimate of a current state of a clock (a component of the clock system), the clock system including: the clock, for providing clock measurements indicating information about the clock; and a state filter, responsive to the clock measurements, for providing the estimate of the current state of the clock using a four-state clock model based on a two-state clock model providing a two-component state, with clock phase and clock fractional frequency as components, and a two-state measure of process noise covariance, the four-state clock model including a four-component state combining the two-component state with a clock error component and a clock error rate component, and including a measure of four-state process noise covariance.
In accord with the second aspect of the invention, the clock measurement may indicate information about the clock phase and clock fractional frequency. Further, the measure of process noise covariance may be a process noise covariance matrix, and the process noise covariance matrix may include as diagonal terms respective variances in the values for each of the four components of the four-component state.
The invention also provides a ranging receiver including a clock system in accord with the second aspect of the invention, the ranging receiver for use in conjunction with beacons of a positioning system, wherein the state filter is adapted for use in the ranging receiver, and wherein the state filter is further responsive to pseudoranges determined from signals provided by the beacons of the positioning system, and wherein the state estimated by the state filter includes the state of the clock as well as the state of the ranging receiver in respect to an aspect of the position of the ranging receiver as a function of time. Further, the clock measurement may indicate information about the clock phase and clock fractional frequency. Further still, the measure of process noise covariance may be a process noise covariance matrix, and the process noise covariance matrix may include as diagonal terms respective variances in the values for each of the four components of the four-component state. In some such applications, the state of the ranging receiver may include as components the clock phase component, the clock fractional frequency component, a clock error component, and a clock error rate component, and may also include either a position component or a velocity component indicating either the position or velocity of the ranging receiver, respectively. In other such applications, the four-state process noise covariance matrix may be based on a definition of a process noise covariance matrix Q given by,
Q=E(wkwkt)
where E( . . . ) indicates taking the mathematical expectation of the indicated argument, and where the wk is a four-component vector indicating process noise. In still other such applications, the four-state process noise covariance matrix may be derived from a two-state process noise covariance for a two-state clock model in a way that preserves the components of the process noise covariance for the two-state clock model, regardless of the manner in which the components of the process noise covariance for the two-state clock model are defined. In still yet other such applications, the ranging receiver may include means for communicating with an external computing facility via wireless communication, and the external computing facility may perform at least some of the computation required to provide a navigation solution and so an estimate of the current state of the ranging receiver based on information the external computing facility receives from the ranging receiver via wireless communication. Finally, the invention also provides a system including a ranging receiver according to the invention for use in a positioning system, and also including the beacons of the positioning system.
Thus, the invention provides an improved model of clock behavior, one in which the conventional clock model states are appended by two more states to account for systematic shifts in frequency. Due to the enlarged state vector and still simple model (a linear model), the tracking of the clock improves. The invention expands the state vector, separately modeling the systematic shift.
With the invention, the quality of post-processing in a ranging receiver is improved, and the accuracy of the positioning provided by the ranging receiver is thereby improved. In addition, the invention allows accounting for how changes in temperature affect the operation of a clock.